WASHINGTON — Facing mounting pressure to respond more aggressively to the migrant crisis unfolding across Europe, the White House on Tuesday said it was re-examining whether it should increase its assistance, including resettling more Syrians in the United States.

As the leaders of Germany and Sweden appealed to other European nations to take their fair share of migrants, American officials hinted that the United States might be moving toward an increase. White House officials said a “working group” at the State Department was “actively considering” a range of options, including refugee resettlement.

The United States currently limits the number of migrants from Syria to 1,500 per year, a tiny fraction of the millions who have flowed out of the war-ravaged country. Officials declined to say whether a sizable increase in the cap had been discussed.

“The international community is looking at the United States right now to determine what additional steps we can take to try to confront, or help Europe confront, this difficult challenge,” said Josh Earnest, the White House press secretary. “We’re certainly mindful of the urgency around increasing the resources and response.”

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Migrants who had crossed the Serbian border into Hungary tried to keep warm at a collection point in Morahalom on Tuesday.Credit
Dan Kitwood/Getty Images

Human rights activists and others have been increasingly critical of the United States for what they say is an inadequate response. Critics also say that the United States has not done enough to end the violence that has sent Syrians fleeing, often at great risk, to Europe.

The United States Committee for Refugees and Immigrants, a nongovernmental agency, has urged President Obama to open American borders to 100,000 Syrians in the next year, in addition to expanding opportunities for resettlement for other migrants.

“We call on our government to continue to show the leadership we have seen in past crises to rescue people who were persecuted,” said Stacie Blake, the director of government relations for the committee. “We cannot stand by and see these photographs of people dying and drowning and running for their lives and not feel compelled to do more.”

David Miliband, the head of the International Rescue Committee and a former British foreign secretary, said on ABC’s “This Week” program on Sunday that accepting 1,500 refugees into the United States was “a minuscule contribution to tackling the human side of this problem.”

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A Syrian from Damascus tried to evade the Hungarian police on Tuesday by sneaking through a forest close to the Serbian border in Morahalom, Hungary.Credit
Dan Kitwood/Getty Images

White House officials took pains on Tuesday to focus on what they said had already been significant assistance from the United States. Mr. Earnest said the United States had provided about $4 billion to help improve conditions at migrant camps in Europe, making America the biggest donor.

Mr. Earnest suggested that the State Department review would also include the possibility of more money to help European nations deal with the influx.

John Kirby, the State Department spokesman, said that the United States had taken in 1,300 Syrians since January and expected several hundred more by the end of the fiscal year on Oct. 1. But he said resettlement was only one option under consideration.

Mr. Kirby said that Secretary of State John Kerry had told his top aides at a staff meeting on Tuesday morning that “if you’ve got good ideas and options” for better helping the international community deal with the crisis, “including here in the United States,” he wanted to hear them.

Ms. Blake, of the Committee for Refugees and Immigrants, said her group wanted the president to increase the overall limit on refugees coming into the United States to 100,000 from 70,000. That would be in addition to the 100,000 Syrians that the committee has urged be admitted.

But Mr. Obama also faces political considerations. Congress would have to approve additional funding for the State Department and the federal Office of Resettlement, which could be difficult when he is already battling the Republican-controlled Congress over other budget priorities.

And Republican lawmakers and presidential candidates have begun to question the wisdom of letting in more Syrians, suggesting that doing so could pose a risk of terrorist attacks.

Traveling in Europe’s River of Migrants

Thousands of migrants and refugees are desperately pushing their way into Europe. A team of New York Times journalists is documenting the journey.

Mr. Earnest said the United States always considers national security issues when admitting refugees. But, he said, “I would not anticipate that a serious policy decision like the one that’s currently being considered by the administration is going to be strongly influenced by the political debate in the Republican presidential primary, regardless of how irresponsible that rhetoric may become.”

On Wednesday, President Jean-Claude Juncker of the European Commission will unveil a divisive proposal calling for refugees to be distributed across the 28-member bloc.

Although the German vice chancellor, Sigmar Gabriel, said this week that his country could accept 500,000 migrants annually for several years, the leaders of Germany and Sweden — which are among the favored destinations of the droves of migrants streaming into Europe — were lobbying for all European Union states to agree to take in a certain number of migrants, relative to each nation’s population and wealth.

The influx has presented Europe with one of its toughest migration challenges in decades, and leaders have been unable to agree on a coherent strategy, intensifying anti-immigrant sentiment in some quarters.

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An advertisement the Danish government placed in the Lebanese newspaper As Safir, beginning with the words, "Denmark has decided to tighten the regulations concerning refugees in a number of areas."Credit
Nabil Mounzer/European Pressphoto Agency

As Britain, France and Germany announced measures on Monday to take in more asylum seekers, Denmark and Hungary sought to dissuade migrants from coming, and Greece made an urgent plea to the European Union for financial aid to help process migrants on the island of Lesbos.

Mr. Juncker is expected to announce a proposal for the distribution of 160,000 migrants across the bloc. But when such a quota proposal was floated in the past, it drew fierce opposition.

Most averse to the idea were countries in Eastern or Central Europe, like Hungary, who consider asylum decisions a matter of national sovereignty and have robustly argued against policies that they fear could undermine the bloc’s security and encourage more migration.

Chancellor Angela Merkel of Germany said that, in addition to negotiating a binding solution for equal distribution of migrants, Europe needed to improve cooperation with Turkey, which has taken in hundreds of thousands of Syrians but has also become a major transit country for those trying to reach northern Europe.

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Camp for Migrants in Hungary

Several hundred people, including children, spent the night in tents at a reception center in an open field in Roszke, Hungary, after crossing into the country from Serbia.

The growing stream of migrants into Europe comes as fighting in Syria has driven more people to flee in recent weeks, and as deteriorating conditions in neighboring countries are pushing many to head straight for Europe, the United Nations refugee agency said on Tuesday.

At the same time, United Nations agencies reported that low levels of funding were forcing them to cut food and other aid to hundreds of thousands of Syrians, another factor pushing many into hazardous journeys to Europe by land and sea.

The Danish government responded to the growing humanitarian crisis with a barely veiled warning to migrants in Lebanon not to come to the prosperous Nordic country.

Danish newspaper advertisements highlighted the stringent regulations and constraints that await migrants: It can take five years to attain permanent residency; there are tough requirements on learning Danish; those who are granted temporary residency permits will not have the right to bring over family members in the first year after they arrive; and recent changes in the country have slashed welfare benefits for them by 50 percent.

In Greece, there were skirmishes overnight between the police and migrants on Lesbos, which has been severely strained by the influx of migrants. The Greek immigration minister, Yiannis Mouzalas, said the situation was “one step before an explosion,” adding that up to 17,000 refugees were on the island, which has a population of 85,000.

Reporting was contributed by Dan Bilefsky from London, Melissa Eddy from Berlin, Niki Kitsantonis from Athens, and Nick Cumming-Bruce from Geneva.

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A version of this article appears in print on September 9, 2015, on Page A10 of the New York edition with the headline: As Migrant Crisis Grows, U.S. Considers Taking In More Syrians . Order Reprints|Today's Paper|Subscribe